Solve for $x$ and $y$ using elimination. ${-2x+6y = -4}$ ${-2x+5y = -5}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${-2x+6y = -4}$ $2x-5y = 5$ Add the top and bottom equations together. ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {-2x+6y = -4}\thinspace$ to find $x$ ${-2x + 6}{(1)}{= -4}$ $-2x+6 = -4$ $-2x+6{-6} = -4{-6}$ $-2x = -10$ $\dfrac{-2x}{{-2}} = \dfrac{-10}{{-2}}$ ${x = 5}$ You can also plug ${y = 1}$ into $\thinspace {-2x+5y = -5}\thinspace$ and get the same answer for $x$ : ${-2x + 5}{(1)}{= -5}$ ${x = 5}$